The proposed research is intended to fill major gaps in the statistical analysis of biomedical data that involve models with patterned means and patterned covariances possibly with missing data. These models arise naturally in the analysis of longitudinal data and some genetics models. Further work on statistical techniques and computer software developed by the Principal Investigator to implement these techniques will be pursued during this grant period with a long range goal of developing highly disseminated, easy to use software (e.g., for SAS or BMDP). Research efforts in this area will include: (1) the completion of documentation and testing of developed computer software; (2) testing of performance characteristics both of the computer software and the underlying statistical procedures; (3) formulating programmable procedures for finding approximate null distributions for explicit MLE patterns; (4) finding asymptotic nonnull distributions under local alternative hypotheses; (5) characterizing the class of linear covariance paterns that are submatrices of linear covariance paterns with explicit MLE; and (6) publishing applications of these new statistical techniques in journals accessible to applied researchers. This proposal addresses the difficulties of developing and implementing statistical techniques which are relatively easy to interpret once the results are in hand even though deriving the results requires sophisticated mathematics. The essence of making statistical techniques available to biomedical researchers is to have software which implements the techniques. When software is not available, researchers resort to alternative (and at times inefficient or incorrect) techniques for which computer software is available.